The Cat in the Box and the Secret of Quantum Possibilities
The Cat in the Box
In 1935 the physicist Erwin Schrödinger dreamed up a strange thought experiment. A cat is locked in a box with a small bit of radioactive material and a poison vial that might break depending on a random quantum event. Until someone opens the box, the rules of quantum mechanics say the cat is both alive and dead at the same time — a superposition of two states. But when we peek, we never see a ghostly half-alive cat. We always find a perfectly living or a perfectly dead cat. Why?
This is the heart of the measurement problem. In standard quantum mechanics, a measurement forces a system to suddenly “collapse” from a blur of possibilities into one single outcome. But what counts as a measurement? Is it when a scientist looks? When a Geiger counter clicks? The problem gets even worse with two particles that once interacted: measuring one seems to instantly fix the properties of the other, even if they are miles apart. The collapse idea feels like a magic trick that nobody ordered.
A group of philosophers and physicists, called modal interpreters, asked a bold question: what if nothing ever collapses? They set out to build an interpretation of quantum mechanics where the wavefunction never jumps — yet we still get a single world full of ordinary, definite things. Their answer is that quantum mechanics is about possibilities, not actualities. And that changes how we think about everything.
What If Nothing Ever Collapses?
In 1972 the philosopher Bas van Fraassen (born 1941) proposed a way out. He said: don’t add a collapse rule to the basic quantum equations. Just let the dynamical state — the wavefunction that obeys the Schrödinger equation — evolve smoothly forever. This state doesn’t tell you what is definitely happening. Instead, it gives you a menu: a list of possible properties and the probabilities for each one.
Van Fraassen then introduced a second ingredient, the value state. The dynamical state says what may be the case. The value state says what actually is the case, right now. A system can have sharp, definite properties even when its dynamical state isn’t focused on one particular answer. For example, a particle could have a real position even if the wavefunction is spread out. This breaks the usual rule that a property is real only if the wavefunction is an eigenstate of that property. Modal interpreters keep half of that rule — “if eigenstate, then definite” — but reject the other half — “only if eigenstate, then definite.”
Van Fraassen called his approach modal because it connects naturally to ideas of possibility and necessity. The wavefunction is like a weather forecast: it tells you the chance of rain or sun, not what is already written in stone. And that’s all we can ever expect from a theory that describes a deeply probabilistic world.
The Magical Split That Picks Out Properties
If the dynamical state only gives probabilities, we still need a rule: which properties get to be definite at any moment? In the 1980s and 1990s, Simon Kochen, a mathematician, and Dennis Dieks, a philosopher of physics, found an answer in a powerful mathematical theorem. They looked at systems made of two parts — say, a particle and a detector. Any pure state of such a pair can be written in a very special way, called the biorthogonal (Schmidt) decomposition. It picks out a unique set of building blocks for each part, like a master key that fits only one lock.
The BDMI (biorthogonal-decomposition modal interpretation) says: the definite properties of each subsystem are exactly the ones that line up with that special decomposition. When you measure something, the interaction with the apparatus creates a correlation, and the magical split automatically selects the pointer position of the detector as a real property. No collapse needed — the right results just pop out as definite values, with the probabilities that Born’s rule gives.
Later, a cousin version called SDMI (spectral-decomposition modal interpretation) generalized this idea. Even when the decomposition is not unique, you can look at the reduced density matrix of a single part and take its spectral decomposition. That tells you which properties are definite and how likely they are. In an ideal measurement, SDMI and BDMI agree: the pointer of the apparatus ends up with a definite reading, and the measured object gets a definite value for the quantity you were checking.
Whose Property Is It, Anyway?
But a puzzle quickly appeared. Imagine a big system made of three parts: α, β, and γ. If you apply the biorthogonal splitting to the pair formed by α and the rest (β+γ), you get a certain set of definite properties for α. If you instead split β and the rest (α+γ), you get a different set for β. Are all these properties true at once? Does α’s property plus β’s property equal a property of the composite system αβ? Usually the rules don’t match up. This is called the property composition problem.
Some philosophers found this so strange that they thought it might kill modal interpretations. If a table’s left half is “green” but the whole table is not “green on the left”, that sounds absurd. Modal interpreters replied: we are just too used to classical thinking. In the quantum world, the question of what properties belong to a whole may be different from the question about its parts. A composite system can have properties that are not simply the sum of the properties of its pieces.
Others took a more radical step. Perspectival modal interpretations (PMI), developed by Gyula Bene and Dennis Dieks, say that properties are relational — they exist only with respect to a reference system. An electron’s position might be definite from my perspective but not from a distant observer’s perspective. Both descriptions are equally real; there is no God’s‑eye view. This idea echoes the relational interpretation of Carlo Rovelli (born 1956), where every property is relative to a specific interaction.
Perspectivalism makes it easier to explain long‑distance correlations without strange instant collapse. When I measure one particle, I define a new perspective. From that perspective, the state of the distant particle changes, but nothing physical travels faster than light — the change is in the relational description, not in some ghostly signal.
When the Environment Decides
Early critics pointed out that in imperfect measurements — the kind we do in real labs — the biorthogonal decomposition might not pick out the exact pointer observable we want. The selected property could be slightly different from the one we think we are measuring. This looked like a serious problem.
But then physicists realized that a measuring device is always open to its environment — a bit of air, a photon, millions of stray particles. This continuous interaction causes decoherence: the reduced state of the apparatus very quickly loses all signs of quantum interference and behaves as if it was in a definite “classical” state. In modal interpretations, decoherence nudges the menu of possibilities so that the pointer observable becomes the preferred definite property. The tiny shift between the ideal and the actual observable becomes too small to notice.
So the environment doesn’t make the wavefunction collapse — it simply selects which properties get to be definite. This marriage of modal ideas with decoherence has become one of the standard ways to defend interpretations without collapse.
A different kind of modal interpretation, the Modal‑Hamiltonian Interpretation (MHI), takes an even simpler path. It says: nature has a preferred observable — the Hamiltonian, which encodes the total energy of a system. Any property that commutes with the Hamiltonian and shares its symmetries can be definite. This rule works without needing the environment to pick the pointer: energy and the constants of motion are always definite. MHI also solves the property composition problem because composite properties are built up from the definite properties of the elemental building blocks, the basic particles.
Why Possibilities Matter More Than Actuality
So why should a twelve‑year‑old care about modal interpretations? Because they touch a question you already live with: is the future open or closed? When you choose between chocolate and strawberry ice cream, it feels like both are real possibilities until you pick one. Classical physics often suggested that everything was determined ahead of time, like a movie that’s already been filmed. Modal quantum mechanics says no — the world is genuinely probabilistic. The present does not force a single future; it only offers a landscape of possibilities, each with a certain weight.
That doesn’t mean “anything goes.” The probabilities are fixed by the laws of quantum mechanics. But the universe you experience is the one where certain possibilities become actual, and there is no hidden film reel deciding those outcomes in advance. This is a powerful way of thinking about freedom, chance, and the limits of prediction. It’s not just about cool physics; it’s about what it means to be an agent in a world that is not yet fully written.
Modal interpretations are still being argued about. No single version has won everyone over. The questions about how to define systems, which properties are preferred, and how to handle relativity are far from settled. But the modal program has taught us something lasting: a theory can be clear, mathematical, and completely about probabilities — and that can be enough. You don’t need a divine list of predetermined facts. You live in a world of real possibilities.
Think about it
- If the universe only gives you probabilities and never a final hidden list, does it still make sense to say “I could have chosen differently” when you pick chocolate over strawberry?
- Suppose two people look at the same particle and, from their different perspectives, it has two different definite positions. Are both descriptions real, or is one of them wrong?
- In your own life, does it ever feel like a moment turns into a definite memory only after someone asks you about it? Could that be like a quantum measurement?
